We consider a number of inverse diffraction problems where different models are compared. Ideal measurements yield Cauchy data , to which corresponds a unique solution. If a convolutional observation map is chosen, uniqueness can no longer be insured. We also briefly examine a non-linear non-invertible observation map , which describes a quadratic detector. In all of these cases we discuss the link between aperture identification and optimal control theory , which leads to regularised functional minimisation. This task can be performed by a discrete gradient algorithm of which we give the flow chart.